# hw20 - Physics 21 Fall, 2009 Solution to HW-20 = 2f = 2...

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Physics 21 Fall, 2009 Solution to HW-20 31.19 You have a resistor of resistance 190 Ω, an inductor of inductance 0.410 H, a capacitor of capacitance 5.50 µ F and a voltage source that has a voltage amplitude of 27.0 volts and an angular frequency of 240 rad/s. The resistor, inductor, capacitor, and voltage source are connected to form an L - R - C series circuit. (a) What is the impedance of the circuit? (b) What is the current amplitude? (c) What is the phase angle of the source voltage with respect to the current? (d) Does the source voltage lag or lead the current? (e) What is the voltage amplitude across the resistor? (f) What is the voltage amplitude across the inductor? (g) What is the voltage amplitudes across the capacitor? (a) The impedence Z of the system is, Z = r R 2 +( ωL 1 ωC ) 2 = s 190 2 + µ 240(0 . 410) 1 240(5 . 5 × 10 6 ) 2 = 686 Ω (b) With V = 27 V the current amplitude is I = V Z = 27 686 =3 . 94 × 10 2 A (c) The phase angle φ = arctan { [ ωL 1 / ( ωC )] /R } is φ = arctan 240(0 . 410) 1 240 (5 . 5 × 10 6 ) 190 = 73 . 9 (d) The previous answer shows that the phase angel is neg- ative, thus the source voltage LAGS the current. (e) The voltage across the resistor is V R = IR = ( 3 . 94 × 10 2 ) × 190 = 7 . 48 V (f) The voltage across the inductor is V L = IX L = ( 3 . 94 × 10 2 ) × 240 × 0 . 410 = 3 . 87 V (g) The voltage across the capacitor is V C = IX C = ( 3 . 94 × 10 2 ) 1 240 (5 . 5 × 10 6 ) =29 . 8V 31.26 In a series L - R - C circuit, the components have the following values: L = 20 . 0 mH, C = 140 nF and R = 350 Ω. The generator has an rms voltage of 120 V and frequency of 1 . 25 kHz. (a) Determine the average power supplied by the generator. (b) Determine the average power dissipated in the resistor. (a) The average power supplied by the generator is

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## This note was uploaded on 11/06/2009 for the course PHYS 21 taught by Professor Hickman during the Spring '07 term at Lehigh University .

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hw20 - Physics 21 Fall, 2009 Solution to HW-20 = 2f = 2...

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